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The multiplicity distributions of charged particles and their combinants for pp collisions at LHC energies are studied within the Multipomeron Exchange Model (MEM) that takes into account the phenomenon of string fusion. It is shown that the use of Gaussian-type distributions for multiplicity distributions at a fixed number of pomerons allows, within the MEM framework, the reproduction of the resulting multiplicity distributions and the oscillatory behavior of combinants, found in the ALICE and CMS pp collision data at LHC energies. It is important that in the proposed approach, the parameters of these Gaussian-type distributions are not considered free, but are calculated from the two-particle correlation function of a single string. [ABSTRACT FROM AUTHOR]

A new method for studying two-particle transverse momentum (PT) correlations in soft hadronic interactions is proposed. It is shown that Monte Carlo models: PYTHIA 6 and Geant4 FTF (FRITIOF), give different predictions for the correlations in proton–proton interactions. The correlations are connected with Schwinger’s mechanism of particle creation. These correlations can be studied in current and future experiments in high energy physics, in particular, at the Nuclotron-based Ion Collider fAcility (NICA).

In this paper, using the concept of multi-pomeron exchange, we develope a Monte Carlo model of interacting quark–gluon strings acting as particle-emitting sources aimed at describing inelastic proton–proton interactions at high energies. The implemented 3D (three-dimensional) dynamics of colour string formation resulted in their finite length in the rapidity space and in the fluctuating event-by-event spatial density. Thus, this results in string cluster formation because of the fusion mechanism and the appearance of long-range multiplicity and mean transverse momentum (mean-pT) correlations in rapidity. We study, via the pseudorapidity dependence, the sensitivity to the details of the 3D dynamical formation of strings for several observables such as the forward–backward correlation coefficient value, strongly intensive quantity, Σ, and the “almost” strongly intensive observable, the variance, σC2, of the distribution of the asymmetry coefficient, C. The strongly intensive quantity Σ is used in this study to suppress trivial statistical fluctuations in the number of particles emitting similar types of sources and to reveal the intrinsic fluctuations of a single source. We demonstrate the connection between Σ and such often used observables as cumulants, factorial cumulants, and σC2. We stress the importance of the contribution of “short” strings and the event asymmetry of the initial conditions on the long-range correlation measures. We argue that string cluster formation because of the fusion mechanism explains the collective effects seen in multiplicity and transverse momentum–multiplicity, ⟨pT⟩–N, long-range correlation functions.

We propose a model for multiple particle production of p p and p ̄ p collisions at high energies. Most of the processes in the model are reasonable physically and/or with reasoning. A fire-ball of a gas, made of grains, is created in the collision and makes an adiabatic and approximately one-dimensional expansion along the collision axis. The fire-ball at the final state, when the grains are free in the fire-ball, is divided into several domains and the thermal equilibrium is realized in each of the domains with different temperatures. Each grain produces several hadrons at the final state. There are two processes of the grains without and with p T (transverse momentum), and the cross-section of the latter process increases with the incident energy. The grains in the domain at the final state obey the extended Maxwell distributions of the temperature Θ , and the hadrons in each grain do that of the temperature T. The values of the adjustable parameters are determined empirically in such a way as to reproduce the data of p T distributions and the rapidity density distributions at various incident energies. The model describes both distributions well at the incident energy of s = 2 2. 4 to 7000 GeV. The local equilibrium in each domain and the adiabatic expansion describe the flat plateau and the shrinkage of the forward region, respectively, of the rapidity density distribution. Another important conclusion is that a simple hydro-dynamical model does not describe the flat plateau of the rapidity density distribution of produced hadrons at high energies. [ABSTRACT FROM AUTHOR]

For high-energy pp scattering described in the framework of a model taking the merger of quark–gluon strings and the formation of string clusters into account, we calculate the strongly intensive variable characterizing correlations between the numbers of particles formed in two rapidity-separated observation intervals. We compare results of the calculations with experimental data of the ALICE collaboration at the Large Hadron Collider. We show that the experimentally observed increase in this variable with increasing initial energy can be explained only if the formation of string clusters consisting of the increasing number of merged strings is taken into account. [ABSTRACT FROM AUTHOR]

A new method for studying two-particle transverse momentum ( P T ) correlations in soft hadronic interactions is proposed. It is shown that Monte Carlo models: PYTHIA 6 and Geant4 FTF (FRITIOF), give different predictions for the correlations in proton–proton interactions. The correlations are connected with Schwinger's mechanism of particle creation. These correlations can be studied in current and future experiments in high energy physics, in particular, at the Nuclotron-based Ion Collider fAcility (NICA). [ABSTRACT FROM AUTHOR]

In this paper, using the concept of multi-pomeron exchange, we develope a Monte Carlo model of interacting quark–gluon strings acting as particle-emitting sources aimed at describing inelastic proton–proton interactions at high energies. The implemented 3D (three-dimensional) dynamics of colour string formation resulted in their finite length in the rapidity space and in the fluctuating event-by-event spatial density. Thus, this results in string cluster formation because of the fusion mechanism and the appearance of long-range multiplicity and mean transverse momentum (mean- p T ) correlations in rapidity. We study, via the pseudorapidity dependence, the sensitivity to the details of the 3D dynamical formation of strings for several observables such as the forward–backward correlation coefficient value, strongly intensive quantity, Σ , and the "almost" strongly intensive observable, the variance, σ C 2 , of the distribution of the asymmetry coefficient, C. The strongly intensive quantity Σ is used in this study to suppress trivial statistical fluctuations in the number of particles emitting similar types of sources and to reveal the intrinsic fluctuations of a single source. We demonstrate the connection between Σ and such often used observables as cumulants, factorial cumulants, and σ C 2 . We stress the importance of the contribution of "short" strings and the event asymmetry of the initial conditions on the long-range correlation measures. We argue that string cluster formation because of the fusion mechanism explains the collective effects seen in multiplicity and transverse momentum–multiplicity, 〈 p T 〉 –N, long-range correlation functions. [ABSTRACT FROM AUTHOR]

In this paper, the nuclear modification factors, RxA, are investigated for pion production in small system collisions, measured by PHENIX experiment at RHIC (Relativistic Heavy Ion Collider). The theoretical framework is the parton transverse momentum kT-factorization formalism for hard processes at small momentum fraction, x. Evidence for collective expansion and thermal effects for pions, produced at equilibrium, is studied based on phenomenological parametrization of blast-wave type in the relaxation time approximation. The dependencies on the centrality and on the projectile species are discussed in terms of the behavior of Cronin peak and the suppression of RxA at large transverse momentum, pT. The multiplicity of produced particles, which is sensitive to the soft sector of the spectra, is also included in the present analysis.

The present paper reports on the methods of the systematic analysis of the high-energy collision distributions—in particular, those adopted by Jean Cleymans. The analysis of data on high-energy collisions, using non-extensive statistics, represents an important part of Jean Cleymans scientific activity in the last decade. The methods of analysis, developed and employed by Cleymans, are discussed and compared with other similar methods. As an example, analyses of a set of the data of proton-proton collisions at the center-of-mass energies, s=0.9 and 7 TeV, are provided applying different methods and the results obtained are discussed. This line of research has the potential to enlarge our understanding of strongly interacting systems and to be continued in the future.

The Unruh effect can be considered a source of particle production. The idea has been widely employed in order to explain multiparticle production in hadronic and heavy-ion collisions at ultrarelativistic energies. The attractive feature of the application of the Unruh effect as a possible mechanism of the multiparticle production is the thermalized spectra of newly produced particles. In the present paper, the total entropy generated by the Unruh effect is calculated within the framework of information theory. In contrast to previous studies, here the calculations are conducted for the finite time of existence of the non-inertial reference frame. In this case, only a finite number of particles are produced. The dependence on the mass of the emitted particles is taken into account. Analytic expression for the entropy of radiated boson and fermion spectra is derived. We study also its asymptotics corresponding to low- and high-acceleration limiting cases. The obtained results can be further generalized to other intrinsic degrees of freedom of the emitted particles, such as spin and electric charge.

In this paper, the nuclear modification factors, R x A , are investigated for pion production in small system collisions, measured by PHENIX experiment at RHIC (Relativistic Heavy Ion Collider). The theoretical framework is the parton transverse momentum k T -factorization formalism for hard processes at small momentum fraction, x. Evidence for collective expansion and thermal effects for pions, produced at equilibrium, is studied based on phenomenological parametrization of blast-wave type in the relaxation time approximation. The dependencies on the centrality and on the projectile species are discussed in terms of the behavior of Cronin peak and the suppression of R x A at large transverse momentum, p T . The multiplicity of produced particles, which is sensitive to the soft sector of the spectra, is also included in the present analysis. [ABSTRACT FROM AUTHOR]

Within the framework of the model with quark-gluon strings (color flux tubes) as sources, the properties of the strongly intense variable Σ , which characterizes the correlations between the number of particles in two observation windows separated in rapidity, are studied. It is shown that, in pp collisions at LHC energies, string fusion effects leading to the formation of string clusters have a significant effect on the behavior of this observable. The experimentally observed changes in this variable with the initial energy and centrality of the pp collision can only be explained by taking into account the formation of string clusters consisting of an increasing number of merged strings. It is demonstrated that the study of the behavior of the Σ observable as a function of the rapidity distance between the centers of the observation windows and the width of these windows with variable experimental conditions using different energies and centralities of pp-collisions makes it possible to extract the parameters of string clusters from the experimental data. [ABSTRACT FROM AUTHOR]

The Unruh effect can be considered a source of particle production. The idea has been widely employed in order to explain multiparticle production in hadronic and heavy-ion collisions at ultrarelativistic energies. The attractive feature of the application of the Unruh effect as a possible mechanism of the multiparticle production is the thermalized spectra of newly produced particles. In the present paper, the total entropy generated by the Unruh effect is calculated within the framework of information theory. In contrast to previous studies, here the calculations are conducted for the finite time of existence of the non-inertial reference frame. In this case, only a finite number of particles are produced. The dependence on the mass of the emitted particles is taken into account. Analytic expression for the entropy of radiated boson and fermion spectra is derived. We study also its asymptotics corresponding to low- and high-acceleration limiting cases. The obtained results can be further generalized to other intrinsic degrees of freedom of the emitted particles, such as spin and electric charge. [ABSTRACT FROM AUTHOR]

The present paper reports on the methods of the systematic analysis of the high-energy collision distributions—in particular, those adopted by Jean Cleymans. The analysis of data on high-energy collisions, using non-extensive statistics, represents an important part of Jean Cleymans scientific activity in the last decade. The methods of analysis, developed and employed by Cleymans, are discussed and compared with other similar methods. As an example, analyses of a set of the data of proton-proton collisions at the center-of-mass energies, s = 0.9 and 7 TeV, are provided applying different methods and the results obtained are discussed. This line of research has the potential to enlarge our understanding of strongly interacting systems and to be continued in the future. [ABSTRACT FROM AUTHOR]

We propose the generalized multipomeron exchange model for multiparticle production in high-energy proton–proton, proton–nucleus and heavy-ion collisions. For all of these systems, we consider collectivity effects based on the quark–gluon string fusion concept, where new types of particle-emitting sources—strings with higher tension—are produced. We obtained the model parameters using the data on the multiplicity dependence of the mean transverse momentum of charged particles in p p and p p ¯ collisions over a wide energy range (from ISR to LHC). We calculated the yields of strange, multi-strange and charm particles as a function of multiplicity for p p , p- P b and P b - P b collisions at the LHC energy and compared the results with the experimental data. [ABSTRACT FROM AUTHOR]

We present a comprehensive insight into counting distributions from the perspective of the combinants extracted from them. In particular, we focus on cases where these combinants exhibit oscillatory behavior that can provide an invaluable new source of information about the dynamics of the process under study. We show that such behavior can be described only by specific combinations of compound distributions based on the Binomial Distribution and provide their analytical forms which can be used in further investigations and which can be helpful in the analysis of all other types of counting distributions. [ABSTRACT FROM AUTHOR]

In this work, the interactions of 7Li nuclei with emulsion at 3 A GeV/c were studied. Multiplicity of the charged secondary particles as well as the charge of the outgoing projectile fragments were measured, while correlations among them are discussed. The values of the total charge of the noninteracting projectile nucleons and the average number of interacting projectile nucleons are estimated. The dependence of the secondary particles on the number of heavily-ionized tracks is analyzed. The results show that interactions of 7Li nuclei with emulsion nuclei exhibit a number of regularities, which had been noted in experiments with lighter nuclei. The absorption of relativistic particles, while increasing the degree of target destruction, is observed. The average multiplicities of the secondary charged particles depend on the impact parameter, as their values increase, while decreasing the impact parameter. The number of secondary charged particles in the heavy-ion interactions depends on the degree of disintegration of the target nuclei. This dependence is not observed in the case of the interaction of hadron with emulsion. The experimental data of the interaction of 7Li are systematically compared with the other interactions at different energies. The results agree with the corresponding results at nearly the same energy. [ABSTRACT FROM AUTHOR]

As shown recently, one can obtain additional information from the measured charged particle multiplicity distributions, P (N) , by extracting information from the modified combinants, C j . This information is encoded in their specific oscillatory behavior, which can be described only by some combinations of compound distributions such as the Binomial Distribution. This idea has been applied to p p and p p ̄ processes thus far. In this note, we show that an even stronger effect is observed in the C j deduced from e + e − collisions. We present its possible explanation in terms of the Generalized Multiplicity Distribution (GMD) proposed some time ago. [ABSTRACT FROM AUTHOR]

In the framework of the quark–gluon string fusion model on the transverse lattice, we study a strongly intensive variable characterizing correlations between the number of particles produced in hadronic interactions in two observation windows separated by a rapidity interval. We show that in the case of independent identical strings, this variable is indeed strongly intensive. It depends only on string characteristics and is independent of trivial so-called volume fluctuations in the string number resulting, in particular, from inevitable impact parameter fluctuations. With string fusion effects causing the production of string clusters with new properties taken into account, this variable turns out to be equal to the weighted average of its values for different string clusters. The weighting coefficients depend on the collision conditions, and the variable loses its strongly intensive character. In the framework of this model in a realistic case with a nonuniform string distribution in the transverse plane, we find explicit analytic formulas for the asymptotic coefficients of long-range correlations between different quantities including an intensive one, the average transverse momentum. We analyze the properties of the obtained correlation coefficients, the studied strongly intensive variable, and also the possibilities of its experimental observation. [ABSTRACT FROM AUTHOR]

Abstract Using the formalism of the light-cone wave function in perturbative QCD together with the hybrid factorization, we compute the cross-section for three particle production at forward rapidities in proton–nucleus collisions. We focus on the quark channel, in which the three produced partons — a quark accompanied by a gluon pair, or two quarks plus one antiquark — are all generated via two successive splittings starting with a quark that was originally collinear with the proton. The three partons are put on-shell by their scattering off the nuclear target, described as a Lorentz-contracted "shockwave". The three-parton component of the quark light-cone wave function that we compute on this occasion is also an ingredient for other interesting calculations, like the next-to-leading order correction to the cross-section for the production of a pair of jets. [ABSTRACT FROM AUTHOR]

Heavy ion collisions quickly form a droplet of quark–gluon plasma (QGP) with a remarkably small viscosity. We give an accessible introduction to how to study this smallest and hottest droplet of liquid made on Earth and why it is so interesting. The physics of heavy ion collisions ranges from highly energetic quarks and gluons described by perturbative QCD to a bath of strongly interacting gluons at lower energy scales. These gluons quickly thermalize and form QGP, while the energetic partons traverse this plasma and end in a shower of particles called jets. Analyzing the final particles in various ways allows us to study the properties of QGP and the complex dynamics of multiscale processes in QCD that govern its formation and evolution, providing what is perhaps the simplest form of complex quantum matter that we know of. Much remains to be understood, and throughout the review big open questions are encountered. [ABSTRACT FROM AUTHOR]

Multiparticle production processes provide valuable information about the mechanism of the conversion of the initial energy of projectiles into a number of secondaries by measuring their multiplicity distributions and their distributions in phase space. They therefore serve as a reference point for more involved measurements. Distributions in phase space are usually investigated using the statistical approach, very successful in general but failing in cases of small colliding systems, small multiplicities, and at the edges of the allowed phase space, in which cases the underlying dynamical effects competing with the statistical distributions take over. We discuss an alternative approach, which applies to the whole phase space without detailed knowledge of dynamics. It is based on a modification of the usual statistics by generalizing it to a superstatistical form. We stress particularly the scaling and self-similar properties of such an approach manifesting themselves as the phenomena of the log-periodic oscillations and oscillations of temperature caused by sound waves in hadronic matter. Concerning the multiplicity distributions we discuss in detail the phenomenon of the oscillatory behavior of the modified combinants apparently observed in experimental data. [ABSTRACT FROM AUTHOR]

In this work we study the pseudorapidity spectra of charged particles produced in proton + proton and proton + antiproton interactions in a wide energy range using the non-extensive Tsallis approach. We evaluate the inelasticity coefficients of the discussed reactions which remain approximately independent of the collision energy.

Different aspects like multiplicity moments, moments and multiplicity fluctuations in terms of scaled variance of the shower particles has been carried out for central events of , and interactions at (4.1-4.5) AGeV/c. Comparison of our results with different experimental analysis of central collisions of emulsion data has been performed whenever available. [ABSTRACT FROM AUTHOR]

We calculate the strongly intensive observables for multiplicities in two rapidity windows in the model with independent identical strings taking into account the charge sign of particles. We express the observables through the string pair correlation functions describing the correlations between the same and opposite sign particles produced in a string decay. We extract these charge-wise string two-particle correlation functions from the ALICE data on the forward-backward correlations and the balance function. Using them we predict the behavior of the charge-wise strongly intensive observables in the model with independent identical strings. We also show that the observable between multiplicities in two acceptance windows separated in rapidity, which is a strongly intensive in the case with independent identical strings, loses this property, when we take into account string fusion effects and a formation of strings of a few different types takes place in a collision. We predict the changes in the behaviour of this observable with energy and collision centrality, arising due to the string fusion phenomena.

The transverse momentum spectra of hadrons produced in high energy collisions can be decomposed into two components: the exponential ("thermal") and the power ("hard") ones. Recently, the H1 Collaboration has discovered that the relative strength of these two components in Deep Inelastic Scattering (DIS) depends drastically upon the global structure of the event - namely, the exponential component is absent in the diffractive events characterized by a rapidity gap. We discuss the possible origin of this effect and speculate that it is linked to confinement. Specifically, we argue that the thermal component is due to the effective event horizon introduced by the confining string, in analogy to the Hawking-Unruh effect. In diffractive events, the t-channel exchange is color-singlet and there is no fragmenting string - so the thermal component is absent. The slope of the soft component of the hadron spectrum in this picture is determined by the saturation momentum that drives the deceleration in the color field, and thus the Hawking-Unruh temperature. We analyze the data on nondiffractive pp collisions and find that the slope of the thermal component of the hadron spectrum is indeed proportional to the saturation momentum. [ABSTRACT FROM AUTHOR]

Presence of unusual azimuthal structures in the particle emission data obtained from the 28Si-Ag/Br interaction at 14.5A GeV and from the 32S-Ag/Br interaction at 200A GeV, are investigated in the framework of the Cherenkov gluon emission and/or Mach shock wave formation in nuclear/partonic medium. Nuclear photographic emulsion technique is used to collect the experimental data. The experiment is compared with the predictions of two simulations, namely (i) the Relativistic Quantum Molecular Dynamics (RQMD) and (ii) the Ultra-relativistic Quantum Molecular Dynamics (UrQMD). A charge reassignment algorithm is implemented over the outputs of the simulations to mimic the Bose-Einstein correlation (BEC) effect. Our analysis confirms presence of jet-like structures in both experiments beyond statistical noise. Such structures are more pronounced in the 32S data than in the 28Si data. [ABSTRACT FROM AUTHOR]

A systematic study of rapidity dispersion parameter as a quantitative measure of clustering of particles has been carried out in the interactions of 16O, 28Si and 32S projectiles at 4.5 A GeV/c with heavy () and light (CNO) groups of targets present in the nuclear emulsion. For all the interactions, the total ensemble of events has been divided into four overlapping multiplicity classes depending on the number of shower particles. For all the interactions and for each multiplicity class, the rapidity dispersion parameter values indicate the occurrence of clusterization during the multiparticle production at Dubna energy. The measured rapidity dispersion parameter values are found to decrease with the increase of average multiplicity for all the interactions. The dependence of rapidity dispersion parameter on the average multiplicity can be successfully described by a relation D(η) = a + b〈ns〉 + c〈ns〉2. The experimental results have been compared with the results obtained from the analysis of Monte Carlo simulated (MC-RAND) events. MC-RAND events show weaker clusterization among the pions in comparison to the experimental data. [ABSTRACT FROM AUTHOR]